Should I provide `iterator` type of an unmodifiable container?

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I'm writing a class which is unmodifiable from outside. It is not 'immutable' since it modifies the contents inside.

I want it to be a Container-interface-compliant container; it can't be Container anyway since it doesn't have a default constructor.

What i'm wondering is, "Should I provide iterator?."

The easiest way is to set iterator to be the same with const_iterator, but I found that lots of people try to iterate a container through iterator, not const_iterator even if they don't modify the value while iterating.

Will it be meaningful providing iterator which can't modify the value?

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